Proposed methodology for the creation of a classification label: a school performance case study

Abstract

Quality in Education is an issue that has been discussed in schools and among their managers, in the media, and in the literature. However, a deeper review of the literature has failed to present techniques dealing with database information techniques capable of obtaining classifications for school performance; nor is there a consensus regarding the definition of “educational quality”. To address the situation, in this paper, we propose a methodology that fits the KDD (Knowledge Discovery in Databases) process to classify teaching in schools. This is done by comparing the grades of the “Prova Brasil”, which is part of the Development Index of Basic Education (IDEB) in Brazil. To illustrate the methodology, it was applied to 17 public elementary schools in the municipality of Araucária, located in the metropolitan region of Curitiba, Parana state. The grades achieved by all students of the initial years (1^st to 5^th year of fundamental teaching) and final years (6^th to 9^th years of fundamental teaching) were considered. In the Data Mining phase, the main phase of the KDD process, three techniques were used comparatively: Artificial Neural Networks, Support Vector Machines, and Genetic Algorithms. Those techniques presented acceptable results in classifying each school represented by a “Performance Classification Label”. Based on this label, the educational managers can have a greater input for procedures to be adopted in each school, and thus set more accurate targets.

Keywords:
School performance; KDD process; Pattern recognition; Real case study

Resumo

A qualidade na educação tem sido objeto de muita discussão, seja nas escolas e entre seus gestores, seja na mídia ou na literatura. No entanto, uma análise mais profunda na literatura parece não indicar técnicas que explorem bancos de dados com a finalidade de obter classificações para o desempenho escolar, nem tampouco há um consenso sobre o que seja “qualidade educacional”. Diante deste contexto, neste artigo, é proposta uma metodologia que se enquadra no processo KDD (Knowledge Discovery in Databases, ou seja, Descoberta de Conhecimento em Bases de Dados) para a classificação do desempenho de instituições de ensino, de forma comparativa, com base nas notas obtidas na Prova Brasil, um dos itens integrantes do Índice de Desenvolvimento da Educação Básica (IDEB) no Brasil. Para ilustrar a metodologia, esta foi aplicada às escolas públicas municipais de Araucária, PR, região metropolitana de Curitiba, PR, num total de 17, que, por ocasião da pesquisa, ofertavam Ensino Fundamental, considerando as notas obtidas pela totalidade dos alunos dos anos iniciais (1º. ao 5º. ano do ensino fundamental) e dos anos finais (6º. ao 9º. ano do ensino fundamental). Na etapa de Data Mining, principal etapa do processo KDD, foram utilizadas três técnicas de forma comparativa para o Reconhecimento de Padrões: Redes Neurais Artificiais; Support Vector Machines; e Algoritmos Genéticos. Essas técnicas apresentaram resultados satisfatórios na classificação das escolas, representados por meio de uma “Etiqueta de Classificação do Desempenho”. Por meio desta etiqueta, os gestores educacionais poderão ter melhor base para definir as medidas a serem adotadas junto a cada escola, podendo definir mais claramente as metas a serem cumpridas.

Palavras-chave:
Desempenho escolar; Processo KDD; Reconhecimento de padrões; Estudo de um caso real

1 Introduction

Nowadays, companies from a wide range of sectors such as production, telecommunications, educational institutions, hospital, have historical information stored in databases. This is natural, because computer media are practical and made for this purpose. However, the task of simply storing data is not sufficient. It is also necessary to verify whether the collected data include relevant information or if there is some knowledge to be discovered.

In the educational field, more specifically, there are assessment instruments of the Federal Government that are generally used to set an index, but can also be used to generate other information for the states, municipalities and the entire school community.

One of these educational databases was used in the present study: the Basic Education Development Index (Índice de Desenvolvimento da Educação Básica (IDEB)). It was used to illustrate a proposed methodology for the creation of the Classification Label.

This proposed methodology emerged to answer address issues such as: How to use real data in the creation of a classification label for different “elements” (in this study, schools); how to obtain a parameter that can be considered “average quality” with these data; and, especially, how to classify an element in the label that does not directly fit any of the classification levels. Furthermore, the case study used here shows that this type of classification label can be highly versatile and be applied to a wide range of fields such as electricity (Van Casteren et al., 2005).

The method presents an easily visualized label. In the context, the Knowledge Discovery in Databases (KDD) process was used, providing comparison patterns.

This label is obtained “by comparison” because it indicates in a group/region the performance of schools on a scale of six levels (A, B, C, D, E and F), where the schools with an “A” rating are the best performers and those with an “F” are the poorest.

To classify these schools, three Operational Research methods were used that are highlighted in the field of educational research: Artificial Neural Networks (ANNs) (Kardan et al., 2013; Yeh & Lo, 2005), Support Vector Machines (SVM) (Huang & Fang, 2013; Wang et al., 2008) and Genetic Algorithms (GA) (Moreno et al., 2012; Meng et al., 2007), comparatively.

This article is organized into five sections, including this introduction. In Section 2, a review of the literature is conducted regarding the general concept of quality, focusing on works in the educational field. Section 3 looks at the concept of educational quality from the viewpoint of Brazilian legislation. The proposed methodology and its illustrative application are presented in Section 4. The final considerations are given in Section 5.

2 Review of the literature: from the general concept of “quality” to works in the educational field

According to Paladini (1995), in prehistoric times, man already sought quality, although its meaning was not clear. Since then, it has been perceived in different fields of knowledge. It can be defined in many ways, depending on where its use is employed, as each concept has several levels of abstraction. Beginning with the etymology of the word “quality”, it stems from the Latin, meaning “of what nature”. In Portuguese, it means “something distinguishable from similar things” (Ferreira, 2001, p. 571).

Due to these several meanings, five approaches are proposed by Garvin (1992), encompassing all the as meanings of quality: transcendental; product-based; production-based; user-based; and value-based. In the transcendental approach, quality is considered innate, i.e., it cannot be precisely defined or measured; it is something that exists or does not exist and is recognized through experience. A point in question is the Rolex watch brand. People only need to hear the name to “know” that these watches are high quality products.

In the product-based approach, quality is measured by the number of characteristics of the product, i.e., the more attributes it has, the higher its quality will be. An example of this is the choice of a new car. Two cars can be compared and a possible differential would be one having air-conditioning while the other does not. Consequently, this item is seen as giving the car more quality.

In the production-based approach, quality is attributed to the characteristics of the product that are in “conformance with requirements”, i.e., error free. A point in question is the production of embroidered T-shirts with a company brand. Put simply, one can ask: “Are all the logos in the right place?” The more T-shirts that are manufactured correctly, the higher the production-based quality will be.

In the user-based approach, quality is gauged by whether the product or service is equal to the user’s expectations. This approach is subjective because user assessment in relation to specifications is how the standard of quality is evaluated. An example of this would be asking: “Is teaching in schools satisfying the needs of students and society?”

Finally, in the value-based approach, quality is understood as the relationship between cost and benefit, i.e., the price that the user/consumer is willing to pay for a product or service. An example of this could be in planning a trip. When considering a location, the user can choose to stay in a hotel with more or fewer “stars” (quality) in its classification.

The definitions of Garvin (1992) show that there is no single “truth” regarding quality and that one or more of the author’s approaches can co-exist in the same scenario. In any case, the author manages to cover all the definitions.

Regarding quality in education, this has been discussed for decades in many countries. Summaries of some of these works are shown below in chronological order.

Research on the quality of education in Indonesia was conducted by Elley (1976). One of the greatest contributions was that the researcher found that children in rural districts learned less than those in urban areas, although no reasons were given for this difference. Furthermore, the author analyzed the working conditions of teachers in order to propose some norms for each region of the country and the country as a whole.

In their pilot study in the United States, Moss et al. (1978) assessed the quality of teaching of engineering during a conference. They used instruments like questionnaires and interviews on two different occasions: before and after the conference. This study sought to verify the opinion of students regarding external evaluations. To the authors, this offered at least one method for measuring quality control better. They concluded that students are not opposed to external evaluations as a way of gauging the quality of these courses in comparison with other institutions in the country.

A model for evaluating teaching methods for decision making regarding the efficiency of the quality of these decisions was developed by Benaim (1984), using a school in Venezuela as a case study. The variables used for the model included teaching and learning resources, the assessment system, the qualifications and appreciation of teachers and tutoring. The authors found that in the method that was developed, the absolute values of these variables should not be measured, but rather their results such as students’ grades and reports by the teaching staff.

Dockrell (1988) conducted a historical review of the assessment systems in Scotland and England, showing the fields of knowledge that are evaluated in each. The researcher found that having quality indexes and not using them is useless, especially when teachers are not aware of these results because it is only when teachers are aware of this information that an impact can be made on education.

A study on the quality of education in Israel was conducted by Inbar (1988), analyzing two moments in the history of the country. First, the author points out that the factors that had a negative influence on the quality of education was the rapid growth of the education system. In twelve years, between 1948 and 1960, the population of the country trebled. The country did not have the necessary infrastructure for this growth, nor did it have enough qualified teachers. Secondly, once these two problems were overcome, the main problem was social inequality.

Carreira & Pinto (2007) pointed out some criteria to be considered when measuring quality of education in Brazil, bearing in mind the democratic perspective and social quality. The aspects they identified included the salaries of teachers and other education professionals, infrastructure and teacher training. All of these aspects are addressed by the Brazilian National Education Plan.

Many works in the literature are concerned with social position for quality in education (Oliveira & Araujo, 2005; Parpala & Lindblom-Ylanne, 2007); analyses of the quality of educational sites (Graells, 1999; Carvalho, 2006); quality of services provided by public educational institutions (Fowler et al., 2011) and evaluations of assessment methods in education (Steil & Barcia, 2006; Birenbaum, 2007; Tillema et al., 2011).

Some works discuss the criteria that should be considered for preparing indicators of quality in education, but do not present methods regarding “how to arrive at” these indicators.

However, there are works that address the quality of services in education, using the ServQUAL statistical method (Figueiredo et al., 2006; Mahapatra & Khan, 2007; Udo et al., 2011; Abari et al., 2011; Ansary et al., 2014). The ServQUAL is a method that indicates quality through several items in services. Through quantitative information, it seeks to express a qualitative analysis. For this purpose, two affirmative statements are used, with one referring to expectations and the other to perceived quality of service. The interviewees evaluate each item in the instrument with options varying from “I totally disagree” to “I totally agree”, marking each option on a five-point or seven-point scale. Statistical elements such as average and standard deviation are used to analyze the responses and verify whether the services meet the expectations and perceptions of the customer (Salomi et al., 2005).

Figueiredo et al. (2006) conducted a study to gauge customer satisfaction regarding quality in language schools, using questionnaires for the SERVQUAL method. They used a numerical evaluation that enabled them to gauge the quality of the services on offer by the institution, highlighting their strong and weak aspects in terms of quality. Among the factors considered were infrastructure, customer services, timekeeping, and teacher qualifications. Mahapatra & Khan (2007) developed an instrument for measuring quality in the field of education (technical teaching institutions) based on the ServQUAL. For this purpose, four Artificial Neural Network topologies were used, with backpropagation as the learning algorithm, to predict quality in education for the different interested parties (students, former students, parents, recruiters, universities, support staff, government, society and administrators). The instrument is validated by factor analysis, followed by the Varimax method. However, like the other works that have been described, the author does not present quality on a hierarchical classification scale. Udo et al. (2011) used the SERVQUAL method to evaluate quality in distance learning in five dimensions (assurance, empathy, responsiveness, reliability and website content). With the exception of reliability, these dimensions influence future intentions to enroll in these courses and student satisfaction.

An evaluation of the post-graduate course at a private university was the application of the SERVQUAL method used by Abari et al. (2011) to gauge the gap between expected and actual quality. According to the authors, the study presented difference meanings for expected and experienced quality. A study at the same level of teaching and with the same variables (tangibles, reliability, responsiveness, assurance and empathy) was conducted by Ansary et al. (2014) in Malaysia to gauge whether gender and nationality influenced the quality of services. The authors found that there was insufficient evidence in terms of gender, but that nationality had a slight influence on the responsiveness of the quality of the service.

The present study differs from the others by presenting, in Section 4, a methodology that uses quantitative information stored in databases to create a school performance label, comparatively, with the KDD process in its context. In Section 3, below, some concepts are presented on quality in education, considering Brazilian legislation.

3 Educational quality and Brazilian legislation

As presented in Section 2, the concept of quality can have many meanings, depending on the context in which it is employed. According to Carreira & Pinto (2007), in education this concept is related to how education is perceived by the person defining it. It is clear that this concept in this field has different meanings, since there are different conceptions of education, many of which differ on a number of points.

The Brazilian Federal Constitution and the Law of Directives and Bases for National Education ensure that teaching must meet with minimum quality standards. Furthermore, the latter affirms that non-compliance with this minimum quality is “in violation of” a student’s right to learn, as stated in the Constitution. The Chamber of Basic Education (Câmara de Educação Básica (CEB)) points out that the transfer of resources and technical assistance to ensure compliance with this right is the obligation of the Federal Government (Brasil, 2010).

In the drive to set minimum standards and attributes regarding the quality of education, the CEB, in its 8/2010 report, indicated that the “Student-cost for Initial Quality” (CAQi) is a possible instrument for clearly presenting the necessary input to guarantee this standard. Therefore, the CAQi should be viewed as “[...] an established option for making the initial steps towards quality feasible, thus its name [...]” (Brasil, 2010).

The CAQi originated during the National Campaign for the Right to Education and, in 2008, came to be considered by the National Education Council as “[...] a strategy of public policy for Brazilian education to overcome the inequalities of education in our country [...]” (Brasil, 2010). This council “[...] understands that the adoption of the CAQi is a decisive step towards addressing these differences and, therefore, the drive for greater equality of educational opportunities for all [...]” (Brasil, 2010). In other words, the concept of quality employed here is directly linked to the perspective of democracy and social quality.

Regarding the CAQi, Carreira & Pinto (2007) assume that the values presented for each step and modality of teaching establish a minimum standard of quality in education and that this will tend to grow as demand for quality increases. In other words, it is a dynamic process. Moreover, the values presented are based on the indispensable attributes for the development of teaching and learning processes, including: salaries of teachers and other education professionals, infrastructure and teacher training, as defined in the National Education Plan.

The CEB highlights some of the factors in the CAQi that are closely related to quality in education, including the size of the educational unit, the number of students per class, time spent by the student in the unit every day (partial or whole) and the appreciation of teaching professionals (initial and ongoing training and career and promotion plans). Thus, the results expected in education are closely linked to the resources available for it, as these are what generate a good working infrastructure, adequate management of teaching and the appreciation of education professionals.

The CEB report finalizes its considerations by indicting that great challenges lie ahead in terms of education quality (Brasil, 2010): to make access to school available to all from kindergarten to high school; to reduce the difference between schools in terms of infrastructure; to implement career and promotion plans; to address the national minimum wage for education professionals and working hours for teachers; to promote initial and ongoing training for teachers; to ensure that the states, the Federal District and municipalities achieve within the next ten years a Basic Education Development Index (IDEB) of at least 6.0 on a scale of 1 to 10; to improve educational management both in schools and in education systems; and to provide adequate funding that is compatible with the demands of modern society.

The IDEB, created by the Brazilian federal government in 2007, is calculated taking into account the results of evaluations conducted by the Anísio Teixeira National Institute of Educational Research and Studies (INEP), pass and failure rates and truancy in public and private schools (INEP, 2011). It is hoped that a school with a high IDEB index will mean that its students are attending class, learning the content of the syllabus and, consequently, not failing.

This index has an indicator for each segment of basic education, i.e., there is an indicator for the early years of schooling (1^st to 5^th year), another for the later years (6^th to 9^th year) and another for high school. This fragments the analysis of the school and, consequently, does not evaluate the performance of the institution as a whole when the school is involved in more than one segment of basic education.

Every two years, a new index is published and everyone can access it through the website of the Ministry of Education. In this evaluation system, one of the instruments is the Prova Brasil, a test sat only by fifth year and ninth year students at public school with a minimum of 20 students enrolled during these years. As this index takes passing grades and truancy into account, in addition to the grade of this specific examination, schools with high grades in the Prova Brasil can have lower IDEB indexes in relation to other schools, as this is only one of three requirements.

Therefore, in the present study, only the Prova Brasil grade is considered (one of the IDEB components) for the creation of the school performance label, as this test is the consequence of several other attributes concerning educational quality indicated by Carreira & Pinto (2007).

4 Methodology for constructing the school performance classification label

The methodology proposed for the creation of the classification label (Góes et al., 2014) considers only the school performance of students in the Prova Brasil test, one of the three IDEB requirements.

To illustrate the methodology, schools that offer Basic Education (1^st to 9^th year) in the same region were analyzed comparatively using the Prova Brasil grades in two subjects: Portuguese (with grades of 0 to 350) and Mathematics (with grades of 0 to 425).

For this purpose, the municipality of Araucária, in the Metropolitan Region of Paraná State was selected. At the time of the study, the municipality had 17 municipal schools that offered basic education (early years, 1^st to 5^th and final years, 6^th to 9^th).

The KDD process was used to support the development of the methodology. This was done in five stages with a view to extracting non-explicit information from the databases prior to application. The stages were data selection, data cleaning or preprocessing, data transformation, application of data mining techniques and knowledge interpretation (Fayyad et al., 1996).

The development of the knowledge is presented in parallel with its application at the 17 schools, with data collected directly from the INEP website, as shown in Chart 1. In this chart, the average grades for each subject (Portuguese and mathematics) are shown for the early years (1^st to 5^th) and the final years (6^th to 9^th).

Chart 1
“Prova Brasil” grades – Araucária, PR.

School	Early Years		Final Years
	Portuguese (0-350)	Mathematics (0-425)	Portuguese (0-350)	Mathematics (0-425)
S1	199.05	219.16	250.40	258.33
S2	176.19	204.38	246.03	243.44
S3	195.01	206.72	238.16	243.29
S4	192.45	215.27	247.60	249.31
S5	190.40	218.36	251.58	258.46
S6	194.40	214.96	239.08	244.28
S7	197.18	218.81	227.29	235.91
S8	183.41	202.93	219.90	229.18
S9	185.14	212.60	255.67	257.05
S10	194.20	214.98	237.33	252.94
S11	183.44	206.16	238.11	240.13
S12	174.40	199.76	240.94	242.30
S13	180.53	205.80	247.05	250.21
S14	183.24	229.39	252.05	267.19
S15	174.47	189.87	262.62	259.40
S16	201.41	238.69	260.56	262.36
S17	198.51	217.58	279.54	284.39

• Fonte: INEP (2011).

An analysis of Chart 1 shows that it is not possible to identify the school that stands out in terms of grades. For instance, S17 has the best grades for the final years and S16 has the best for the early years. Likewise, S15 and S12 have the worst grades for the early years, while S8 has the poorest for the final years.

In the proposed methodology, the schools are classified comparatively, indicating their performance in the Prova Brasil on a six-level scale (A, B, C, D, E and F). for this purpose, the data were organized into individual charts with four classes of classification: C₁ – grades in the Portuguese language test for the early years; C₂ – grades in the mathematics test for the early years; C₃ – grades in the Portuguese language test for the final years; and C₄ – grades in the mathematics test for the final years.

Thus: 174.40 $\le$C₁$\le$ 201.41; 189.87 $\le$ C₂$\le$ 238.69; 219.90 $\le$ C₃$\le$ 279.54; and 229.18 $\le$C_{4 $\le$}284.39. For example, the data for S1 are presented in Chart 2, where C₁= 199.05; C₂ = 219.16; C₃= 250.40 and C₄ = 258.33.

Chart 2
“Prova Brasil” grades for school S1.

Level of Teaching	Subject
	Portuguese	Mathematics
Early Years	199.05	219.16
Final Years	250.40	258.33

Likewise, the charts were prepared for each of the 17 schools. Chart 3 shows the average value for each classification, i.e., for each class C_i the average was calculated in relation to all the schools.

Chart 3
Average grades of the “Prova Brasil” in the selected region.

Level of Teaching	Subject
	Portuguese	Mathematics
Early Years	188.44	212.67
Final Years	246.70	251.66

With the average values defined, it was possible to define the values that delimit the six levels of the label, with “Level A” for best performance and “Level F” for poorest, with the values of the labels varying in according with the limits of each C_i, i = 1, ..., 4, presented in Figure 1.

Figure 1
Comparative performance classification label.

The upper limit of each classification level (Figure 1) was defined as follows: upp lim A and upp lim B were determined as such for C_i, (upp lim A – upp lim A) = (upp lim A – upp lim B) = (upp lim B – upp lim C). The same occurs in all the D, E and F levels: (upp lim C – upp lim D) = (upp lim D – upp lim E) = (upp lim E – upp lim F).

Therefore, with the creation of the classification label for performance in the Prova Brasil, it is clear that it is necessary to define at which level each school should be included (Figure 1, Chart 1). However, of the 17 schools in question, only one fits directly into a level of the label. This is S5, which fits into Level C, i.e., S5 is automatically classified as having “C” quality. Figure 2 shows that S5 has 188.44 $\le$ C₁ = 190.40 $\le$ 192.76; 212.67$\le$C₂=218.36$\le$ 221.34; 246.70 $\le$ C₃ = 251.58 $\le$ 257.65; and 251.66 $\le$C₄ = 258.46 $\le$ 262.57.

Figure 2
School S5 classified (with peformance level “C”) directly to the label.

The other schools cannot be classified directly. For instance, for S4, the values for C₁, C₂ and C₃ fit into Level C of the school performance label, but C₄ belongs to Level B. thus, the question we have to face is how to define the classification of the other schools.

To answer this question, data mining techniques were used to define the classifications of the label. Nevertheless, to apply the techniques it is necessary to conduct a preliminary change of scale (data transformation) in the data extracted from the INEP website (Chart 4). This change of scale occurred through the algorithm presented in Figure 3, below, where the new values for X(i, j) are obtained through the current values. Thus, each new X(i, j) element is presented in Chart 4.

Chart 4
“Prova Brasil” grades following transformation.

School	Early Years		Final Years
	Portuguese	Mathematics	Portuguese	Mathematics
S1	0.09	0.40	0.49	0.47
S2	0.93	0.70	0.56	0.74
S3	0.24	0.65	0.69	0.74
S4	0.33	0.48	0.54	0.64
S5	0.41	0.42	0.47	0.47
S6	0.26	0.49	0.68	0.73
S7	0.16	0.41	0.88	0.88
S8	0.67	0.73	1.00	1.00
S9	0.60	0.53	0.40	0.50
S10	0.27	0.49	0.71	0.57
S11	0.67	0.67	0.69	0.80
S12	1.00	0.80	0.65	0.76
S13	0.77	0.67	0.54	0.62
S14	0.67	0.19	0.46	0.31
S15	1.00	1.00	0.28	0.45
S16	0.00	0.00	0.32	0.40
S17	0.11	0.43	0.00	0.00

Figure 3
Change of scale for the data in Chart 1.

Thus, the data mining techniques are applied to classify the 16 unclassified schools.

4.1 Data mining techniques

The Data Mining stage is the most important of the KDD process because it is here that the pattern recognition techniques are applied, through exact, heuristic or meta-heuristic procedures. The techniques used to classify the 16 schools that could not be directly classified in the classification label were Artificial Neural networks (Haykin, 1999; Mitchell, 1997), SVM (Vapnik, 1995, 1998; Burges, 1998) and Genetic Algorithms (Holland, 1992; Goldberg, 1989).

The common characteristics of all three techniques are those that were used to assess the learning, stratified three-fold cross validation (each application is referred to here as a stage), i.e., the set of data for training were divided into two subsets: 2/3 for the training set and 1/3 for the test set. Thus, as there are six classification levels (ranging from A to F, with 60 records per level created fictitiously) there are 360 records, of which 240 are used for training and 120 for tests. As they are stratified, each set (training and test0 is formed by classes (A to F) with the same quantity of elements.

Furthermore, the training of each technique occurred five times (phases), one training for each class seeking to identify whether the record belongs to a determined class. Thus, the training was conducted for class A, making the network “learn” what constitutes a class A record (value close to 0) and what does not (value close to 1, i.e., B, C, D, E and F). Then, removing the data of set A, already classified, another training is conducted for class B, making the network “learn” what constitutes a class B record and what does not (C, D, E and F) and so forth for classes C, D and E. During the final training (class E), when a record is not classified as E, it is automatically classified as F (last class) (Steiner et al., 2006).

Therefore, when classifying a new record, it has to be “presented” to all the phases, thereby obtaining its classification. It should be highlighted that the equipment used for the tests was an Intel® Core™ i5, laptop with a 2.27GHz processor and 4GB RAM memory. The execution times for all the tests were less than five seconds.

The particular characteristics of each technique are now presented (all of them are well known, and further details are unnecessary) in addition to their particularities in the application.

4.1.1 Artificial Neural Networks (ANNs)

In the application of ANNs, the backpropagation learning algorithm was used, implemented using Visual Basic 6.0. Each ANN had four inputs (C₁, C₂, C₃ and C₄), a hidden layer (with the number of neurons varying from “1” to “20”) and a neuron in the output layer, indicating the class and sigmoid (logistic) activation function (logistic) in all the neurons.

The network was trained five times, with a random variation of the set of weights, in an interval of (-1, 1). There were a total of 1500 tests (3 stages x 5 sets of initial weights x 20 quantities of neurons in the hidden layer x 5 classification levels. Each training was finalized when the following three conditions were achieved: 1000 iteractions; average squared error less than or equal to 10^-4; or number of classified records incorrectly equal to zero.

In this application, the success rate in the training of the technique was 100%. For the test, considering the three stages, the success rate was 98.89%. The results of the classification of the schools through the application of this technique are shown in Chart 5.

Chart 5
Result of the classification of schools (ANN).

School	Three-fold Method
	1st stage	2nd stage	3rd stage	Classification by vote
S1	C	C	B	C
S2	E	E	E	E
S3	D	D	D	D
S4	C	C	C	C
S5	C	C	C	C
S6	C	C	D	C
S7	D	D	D	D
S8	E	E	E	E
S9	C	C	C	C
S10	C	C	C	C
S11	E	E	D	E
S12	F	F	E	F
S13	D	D	D	D
S14	E	C	C	C
S15	F	D	E	F
S16	B	B	B	B
S17	A	A	A	A

In Chart 5 and the others that will be presented below, the “Classification by vote” column indicates the classification of the highest occurrence in the previous columns. When there is no classification with a higher occurrence, as is the case for E15, the classification is defined by the poorest placing of the three stages.

Although S5 had already been defined, as it was directly classified to the label (as shown above), it was also introduced to the networks to confirm its classification. Thus, through the classification obtained by the ANNs, there is one school with an “A” classification, one with a “B” classification, seven with a “C” classification, three with a “D” classification, three with an “E” classification and two with an “F” classification.

4.1.2 Support vector machines

The SVM technique seeks a plane that has the same distance for elements of both classes, using a Kernel function (which calculates the classification function) for sets in which the data are not linearly separable. This is done by projecting the data into the “characteristics space”, where they can be separated linearly through an extra dimension. Thus, despite the data not being linearly separable in the pattern input space, they will be in the characteristics space, as shown in Figure 4 (Vapnik, 1995, 1998; Burges, 1998).

Figure 4
Inputs and characteristics space. Source: Góes et al. (2014).

For the application of the SVM technique, the svmtrain function of MATLAB 7.9.0 software was used, with the following parameters: “kernel function: linear”; “optimization method: Sequential Minimal Optimization”; “tolerance for training method: 10^-3”; “kernel multilayer perceptron: [-1, 1]”.

Furthermore, two matrices were used with the arguments: “Examples” and “Response”, in accordance with Equation 1, below. The “Examples” matrix has four inputs C_i (C₁, C₂, C₃ and C₄) in its columns and the “Response” matrix has only one column with the value of the interval for each of the patterns (“Examples”), i.e., classes “A” to “F”.

Training = svmtrain (Examples, Response)(1)

Then, the test set, described here as the “NewExamples” matrix, and the result of the “Training” with the svmclassify, as shown in Equation 2, were used to verify the percentage of correct classifications of these new data.

Classification = svmclassify (Training, NewExamples)(2)

It should be emphasized that the arguments used in the training for the svmtrain function are the default of Matlab 7.9.0, as the sets of levels of the performance classification label are separable by a hyperplane. Fifteen tests were conducted (3 stages x 5 classification levels). The success rate in the training was 100%, considering the three stages of the three-fold method, and 100% in the test. Chart 6, below, shows the results of the classification of the schools obtained through the application of SVM.

Chart 6
Result of the classification of schools (SVM).

School	Three-fold Method
	1st stage	2nd stage	3rd stage	Classification by vote
S1	B	B	B	B
S2	E	E	E	E
S3	D	D	D	D
S4	C	C	C	C
S5	C	C	C	C
S6	D	D	D	D
S7	D	D	D	D
S8	F	F	F	F
S9	C	C	C	C
S10	C	C	C	C
S11	E	E	E	E
S12	E	E	E	E
S13	D	D	D	D
S14	C	C	C	C
S15	D	D	E	D
S16	A	B	A	A
S17	A	A	A	A

Chart 6 provides the following Classification by vote for the schools: two with an “A” classification, one with a “B” classification, five with a “C” classification, five with a “D” classification, three with an “E” classification and one with an “F” classification. It should be emphasized that this technique also correctly classified S5, which had already been directly classified in the performance label.

4.1.3 Genetic algorithm

The GA was used to determine a hyperplane in such a way that in each hyperspace determined would contain only one of the sets of each of the five phases of application at each stage, in accordance with the application method of the technique. It should be highlighted that the training sets as defined are linearly separable.

The value of the fitness function is derived from the algorithm that determines four points that define the hyperplane, in which the coordinates of each point are the alleles of individuals. Each individual is composed of 16 alleles with values belonging to the set of real numbers. Thus, the first four alleles represent the coordinates of a point denominated P₁. The next four alleles are the coordinates of point P₂. The next four are the coordinates of point P₃, and the last four are the coordinates of point P₄. There is also the fitness calculation that takes into consideration the difference of the distances between two points (in different sets) that are closest to the hyperplane. The greater the difference between the distances, the greater the penalty applied to the fitness.

Thus, Figure 5 presents this algorithm for calculating fitness, in which X is a vector in which each coordinate represents an allele of the individual in the population; CL₁ is the set of data for “Class₁” (e.g., “A”) and CL₂ is the set of data for “Class₂”; (not “A”) are the sets for training; k is an element that belongs to Class_1$\cup$Class₂; EP(α) is the equation of the plane defined by P₁, P₂, P₃ and P₄.

Figure 5
Pseudo-code for fitness calculation.

Concerning the algorithm presented in Figure 5, the following observations were made:

1. i

   If k$\in$CL₁ then k should belong to the hyperspace inferior to $\alpha$, and so EP(k) should have a negative value;

2. ii

   If k$\in$CL₂ then k should belong to the hyperspace superior to $\alpha$, and so EP(k) should have a positive value;

3. iii

   Dist₁ and Dist₂ are initialized with high values so that the algorithm determines whether the hyperplane is equidistant or closely equidistant to the training sets (CL₁ and CL₂).

To apply the GA, a penalty of 0.1 and the toolbox of Matblab 7.9.0: gatoo were used. The arguments for the training were the defaults that obtained the best results, with some shown as follows: “population type: double vector”; “population size: 20”; “fitness scaling: rank”; “crossover fraction: 0.8”; “crossover function: scattered”; “stopping criteria (generations): 100”; stopping criteria (stall generations): 50”; and “stopping criteria (function tolerance): 10^-6”. The three stopping criteria were used in such a way that when one of them was achieved, the procedure was finalized.

It should be remembered that the “crossover scattered” works as follows: the crossover default function creates a random binary vector and selects the genes where the vector is “1” of the first factor and the genes where the vector is a “0” of the second father, and combines the genes to form a son. For instance, if p₁ and p₂ are the fathers: p₁ = [a b c d e f g h]; p₂ = [1 2 3 4 5 6 7 8] and the binary vector is [1 1 0 0 1 0 0 0], the function will return to the second son: [a b 3 4 and 6 7 8].

A total of 45 tests were conducted (three stages of the three-fold method x five classification phases, “A” to “F” x three tests with different populations) with the parameters as described above.

The success rate of the training was also 100%, considering the three stages of the three-fold method, and 99.44% in the test. The results of the classification of the schools obtained through the application of this technique are shown in Chart 7. Here, S5 also confirmed its classification. Therefore, there is one school with classification “A”, one with classification “B”, five with classification “C”, five with classification “D”, two with classification “E” and three with classification “F”.

Chart 7
Result of classification of schools (GA).

School	Three-fold Method
	1st stage	2nd stage	3rd stage	Classification by vote
S1	C	B	C	C
S2	E	F	E	F
S3	C	D	D	D
S4	C	C	C	C
S5	C	C	C	C
S6	C	D	D	D
S7	C	D	D	D
S8	F	E	E	E
S9	D	C	C	C
S10	C	D	D	D
S11	D	D	E	D
S12	E	F	F	F
S13	E	E	D	E
S14	B	C	A	C
S15	E	F	D	F
S16	B	B	B	B
S17	A	A	B	A

4.2 Analysis of the results

The analysis of the results, the last stage of the KDD process, is conducted by comparing the classifications obtained using the three techniques. The results of the classifications from the three techniques are shown in Chart 8 (the column labeled “Classification by vote” in Charts 5 to 7). Furthermore, in this chart there is also a column labeled “Classification by vote” that indicates the result of the largest occurrence among the three techniques, which in this analysis we accepted as the most adequate result for the problem in question.

Chart 8
Comparison of the results of the ANN, SVM and GA techniques.

School	ANN	SVM	GA	Classification by vote
S1	C	B	C	C
S2	E	E	F	E
S3	D	D	D	D
S4	C	C	C	C
S5	C	C	C	C
S6	C	D	D	D
S7	D	D	D	D
S8	E	F	E	E
S9	C	C	C	C
S10	C	C	D	C
S11	E	E	D	E
S12	F	E	F	F
S13	D	D	E	D
S14	C	C	C	C
S15	F	D	F	F
S16	B	A	B	B
S17	A	A	A	A

Analyzing this chart, of the 17 schools 7 (S3, S4, S5, S7, S9, S14 and S17) had the same classification using all the techniques. The others had equal classification in only two of the techniques. One of these (S6) had the same classification using SVM and GA; five (S1, S8, S12, S15 and S14) had the same classification using ANN and GA; and four (S2, S10, S11 and S13) had the same classification using ANN and SVM.

Comparing each technique with the classification that is accepted as adequate (column labeled “Classification by vote”), for the SVM there are five schools (S1, S8, S12, S15 and S16) with classifications that are different from those presented in the “Classification by vote column”, with four of these at neighboring levels. The school with a classification at a non-neighboring level was S15, with a “D” classification, while the one accepted as correct was “F”. For the GA technique, there are four schools (S2, S10, S11 and S13) with different classifications from the “Classification by vote” column, but all of these are at neighboring levels.

Finally, the ANN technique has only one school (S6) with a different classification, but at a neighboring level, i.e., the classification obtained using this technique was “C”, while the one accepted as correct was “D”. This is the technique that came closest to the result that is accepted as correct when the three techniques are compared.

Thus, the adequate classification of the schools, as shown in Figure 6, is: one with an “A” classification, one with a “B” classification, six with a “C” classification, four with “D”, three with “E” and two with “F” (Figure 6).

Figure 6
Classification label of the schools (C₁ – Portuguese grades in the early years; C₂ – Mathematics grades in the early years; C₃ – Portuguese grades in the final years; and C₄ – Mathematics grades in the final years).

Returning to the questions raised at the beginning of this article, where it was said that it was not possible to indicate the best school only by analyzing their performance in the Prova Brasil, given that S17 had the best results in the final years and S16 in the early years, the performance label indicates that the best school is S17, with an “A” classification. This is followed by S16, with a “B” classification. The same is true regarding the schools with the poorest performance in the Prova Brasil, with S15 and S12 having the poorest grades in the early years and S8 in the final years. The label indicates that S8 has an “E” classification and S12 and S15 have an “F” classification.

5 Final considerations

As commented in the introduction to this article, this study seeks to answer question regarding how to use real data to create a label, how to define an “average” reference for the classification label and how to classify an element in the classification label that does not directly fit any classification level.

To answer the first question, data were collected from the INEP (2011). With the aid of the KDD process, an attempt was made to discover knowledge in the databases in question. The second question is answered by determining the upper limit of the “C” level of the label through the average of the individual charts of each element “comparatively”, as a group/region is analyzed. In other words, relative rather than absolute results are obtained. It is also due to these individual figures, where the classes are defined by Ci, that the proposed methodology is considered versatile.

To answer the third and last question, the present study used three techniques (ANN, GA and SVM), all of which are related to pattern classifications. The ANN technique had the best performance for this case study.

Regarding the case study, the proposed methodology reveals unobserved knowledge when analyzing only the IDEB index (Chart 9). An example of this is the fact that S12 has a higher IDEB at both levels of basic education (early years and final years) than S2, but considering only the Prova Brasil grades and applying the proposed methodology, the classification is exactly the opposite: S2 has an “E” classification and S12 has an “F” classification. The same occurs in the case of schools S17 and S14.

Chart 9
IDEB of schools in the study.

School	IDEB		Average IDEB	Classification: Proposed methodology
	Early Years	Final Years
S1	4.90	4.00	4.45	C
S2	4.20	3.10	3.65	E
S3	4.60	3.20	3.90	D
S4	4.50	3.70	4.10	C
S5	4.90	4.20	4.55	C
S6	5.00	3.90	4.45	D
S7	5.30	3.40	4.35	D
S8	4.40	3.80	4.10	E
S9	5.00	4.30	4.65	C
S10	4.70	4.00	4.35	C
S11	4.50	3.60	4.05	E
S12	4.60	3.20	3.90	F
S13	4.20	4.20	4.20	D
S14	5.40	5.00	5.20	C
S15	4.10	4.30	4.20	F
S16	5.50	4.40	4.95	B
S17	5.30	5.00	5.15	A

This means that the IDEB does not identify the school were the student have the best performance, which is the criterion considered by most of the population to define a “good school”.

With the classification label based on performance in the Prova Brasil, it is possible to view learning in basic education (1st to 9th year) in comparison with the others and also classify the school not considering truancy and failure rates.

It is worth highlighting that for many researchers in the field of education it is clear that “educational quality” depends on other factors such as the criteria presented by the cost-benefit per student, size of the school, “student-class” ratio and “student-teacher” ratio, initial and ongoing teacher training, school management, appreciation of education professionals and other factors.

In this article, we consider performance in tests such as the Prova Brasil as reflecting these factors, i.e., it is a consequence, as evaluation is fundamental to the teaching and learning process.it is through assessment that the school community can seek ways of improving the quality of education.

Thus, the application of this method for creating school performance labels comparatively through performance in the Prova Brasil presented non-explicit knowledge when the grades of this assessment were analyzed, showing the importance of the KDD process in educational databases and that it is important to further the analysis of this educational quality indicator.

An alternative for using the proposed method would be to create a label from grades in other official examinations administered by the federal/state/municipal government or a specific examination prepared for this purpose based on the data that is considered important when seeking to improve students’ levels of school and scientific knowledge.

Finally, due to the versatility of the method proposed in this study, there remains a great deal to be explored with different techniques in different fields. It would be desirable to develop an article that addresses the concepts of quality in detail, together with quality indicators in education that currently exist and a “translation” to a language of operations for the themes and concepts in the field of teaching.

Acknowledgements

The second author is grateful to CNPq for scholarship (number 301934/2011-8).

• Financial support: None.

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Publication Dates

• Publication in this collection
  22 Mar 2016
• Date of issue
  Jan-Mar 2016

History

• Received
  09 July 2013
• Accepted
  23 Oct 2015